Data analyses

Home range size, length, shift and overlap, and pasture use were calculated for each possum for both the pre-reduction and post-reduction monitoring periods. Before these analyses were undertaken, the GPS-collar data were evaluated for location accuracy. Fixes with Horizontal Dilution of Precision (HDOP) values greater than 10 (Sirtrack®, 2010) were visually assessed against previous and subsequent fixes, to determine if a possum could reasonably reach these locations between fix intervals (Yockney et al., 2013). Overall, the proportion of high HDOP fixes was very low (<5%) and no fixes were identified as being behaviourally unrealistic. The mean number of fixes obtained per

possum was then calculated for each monitoring event, to determine whether there were differences in sampling effort between individuals.

Prior to undertaking home range analyses, incremental area analyses are recommended to confirm that home ranges are fully revealed within the timeframe of monitoring and therefore comparisons are not biased (Laver and Kelly, 2008; Metsers et al., 2010; Recio et al., 2010). Home ranges were considered to be fully revealed if 95% of a home range was obtained within the monitoring timeframe (i.e., additional location fixes did not increase home range size) (Asari et al., 2010; Metsers et al., 2010; Recio et al., 2010). This was determined by carrying out incremental area analysis of 95% Kernel Density Estimates (KDE) in Ranges8 (Kenward et al., 2008; Laver and Kelly, 2008) and visually establishing if an asymptote was reached (Laver and Kelly, 2008; Recio et al., 2010). This information was then collated to determine the percentage of possums at each site that fully revealed their home ranges within the monitoring period, as well as the mean number of fixes required for home ranges to be fully revealed. However, with respect to the remaining home range estimations, the aim was to assess changes in home range utilisation. Therefore, limiting analyses to only possums that revealed the extent of their home ranges may have resulted in the removal of potentially useful data. As such, possums with an equal sampling effort between events (i.e., there was a similar number of fixes before density reduction as after density reduction, to ensure unbiased comparisons), were also included in these analyses.

Home range size was estimated in Ranges8 (Version 2.7) using 95% and 50% (core) KDE, and 100% Minimum Convex Polygons (MCP) (Kenward et al., 2008). Analyses using fixed kernels with Least Squares Cross Validation (LSCV) bandwidth is recommended for KDE (Seaman et al., 1999). However, this technique often results in under-smoothing and the creation of numerous small perimeters around individual data points, which do not appear to have any behavioural relevance (Blundell et al., 2001; Jones et al., 1996; Kie et al., 2010). This was also the case when LSCV was employed in this study. Analyses using fixed smoothing with reference bandwidth solve this excessive fragmentation issue and therefore more accurately estimate home ranges in these circumstances (Blundell et al., 2001; Jones et al., 1996; Kie et al., 2010). Consequently, reference bandwidth was employed in this study, which also eliminated the excessive fragmentation (see Section 2.6.4: Home range estimation in Chapter 2: General Methods).

One hundred percent MCP were calculated to identify longer distance forays that are excluded using KDE, using a harmonic mean peel centre (Blackie et al., 2010; Kenward et al., 2008). Home range length was calculated in the GIS program ESRI® ArcMap™ (Version 9.3; ESRI, 2008), by measuring the maximum distance across each MCP. Home range shift was also assessed in ArcMap™, by determining the centroid of the 50% KDE before reduction and following reduction,

and calculating the distance between these two points (Janmaat et al., 2009; Rasiulis et al., 2012). To estimate the timing of any changes in movement patterns at Manipulated Site 1, 95% KDE, 50% KDE and MCP home ranges were also calculated for each week of the two monitoring periods (a total of 10 weeks). The weekly percent utilisation of the total home range of the given monitoring period was then calculated, to allow relative comparisons in home range size across individuals and between weeks. The idea being that a peak in utilisation might indicate a point of change in movement patterns. Some weekly values were greater than 100% for the kernel density estimates, due to the smoothing function of this technique resulting in greater weekly sizes than that for the entire monitoring period.

Home range overlap between collared individuals was calculated in Ranges8 for the 95% and 50% KDE, giving the number of overlaps and percent overlap in home range area (Kenward et al., 2008). The area of a home range that did not overlap with any other collared possum (the ‘exclusive area’) was also calculated for each study animal, by exporting the data into ArcMap™ and carrying out overlay procedures (Hoset et al., 2008). For the percent overlap analyses, as the whole population was unable to be collared, the total area of an individual’s home range that overlapped with the home ranges of all other possums in the population was unable to be calculated. Instead, the percent overlap between each pair of collared possums was established. This was only carried out when overlap between possums occurred (i.e., zero overlaps were not included in the analysis). This analysis is therefore considered to provide a relative comparison of the degree of overlap between any two possums at each of the sites (when overlap occurs). To assess pasture use, the percentage of 95% KDE fixes within pasture habitat was calculated.

Count data (i.e., number of fixes, number of fixes until home range revealed and number of home range overlaps) were all analysed using generalised linear mixed-effect (GLMM) models, with a Poisson error structure and logarithmic link function (Crawley, 2007). Proportional data (i.e., percent home range overlap, exclusive area and pasture use) were all analysed using GLMM models with a binomial error structure and logit link function (Crawley, 2007). Continuous data (home range size, home range shift and weekly home range utilisation – as >100% utilisation could be achieved) were analysed using linear mixed-effect models, with a normal (Gaussian) error structure and an identity link function (Crawley, 2007). Individual possum identity was included in each model as a random effect, as well as their change between events (i.e., before and after density reduction) to account for any temporal autocorrelation. Continuous data were natural log transformed when the model residuals exhibited heteroscedasticity.

Models for all response variables were run in the statistical program R (Version 2.15.1, Woodroffe et al., 2006b) with the following combinations of fixed effects: (1) a null model with

intercept only; (2) a model that considered event (before or after density reduction); (3) a model that considered bodyweight (which was measured in kilograms); (4) a model that considered sex (male or female); and (5) a model that considered the interaction between sex and event (to allow an assessment of any variations in spatial perturbation between sexes). An exception to this was the home range shift analyses, which produced only one measurement for each individual and not a value for each event. The model set for this variable was therefore run with a ‘Site’ fixed effect instead of an ‘Event’ fixed effect. This allowed comparisons in home range shift between all three sites. Another exception was the weekly home range analyses, where the model set was run with models 1 – 4 above, as well as a week model (Weeks 1 – 5) and models investigating interactions between week, event and sex.

All model sets were ranked using sample size corrected Akaike Information Criterion (AICc), where the weights of all models in the set sum to one and the model with the highest Akaike Weight is considered to have the best fit for the available data (Anderson, 2008; Burnham and Anderson, 2002). Support for each model was evaluated by assessing the change in AICc from the best model

(ΔAICc) (Anderson, 2008; Burnham and Anderson, 2002). Models with a change of approximately less than two from the best model have substantial empirical support, models with a change of 4 – 7 have considerably less support and models with a change of greater than 10 have essentially no support (Burnham and Anderson, 2002). Each model set was assessed for ‘pretending variables’, whereby the addition of a variable does not change the deviance and therefore the fit of the model, skewing and biasing Akaike weights, but none were identified (Anderson, 2008). Due to differences in habitat type and initial possum densities between sites, and since the study was not replicated in the same year, the data from the three sites were analysed separately (with the exception of home range shift as discussed above).

5.4

Results